How does ICM influence your pushing range?

We have asked you, if you would push the hand in that situation if you assume that your opponents are playing well and understand ICM. We also wanted to know the following things: How important is ICM in the example? What factors are crucial? How does ICM influence your decision in different situations or in other SNG-types?

Let's just analyze the situation.

At the Beginning, we take a look at the chip equity. We assume, that ICM does not exist at all and the players are looking for profitable cEV spots to increase their stacks (like in a cash game).

Without considering ICM and risk premium, your pushing and calling ranges would look like this, according to the nash equilibrium:

You can see, that a push with T3s would lose you 0.32BB (0.32*8,000 = 2,560 chips). Without ICM (in a cash game) this move would not be profitable.

Because of the payout structure of a SNG, you need to take ICM effects into consideration, because it influences the value of your stack and of the stacks of your opponents.

In this case your push with T3s would win you 0.16% of the prize pool. In a $15 180-player SNG that would correspond to a profit of $4.

The reason for such a extreme outcome is the very small stack of the CO (who folded in that hand). Due to the relatively big pay jumps, it is very profitable for the SB and BB just to wait, until the short stack busts out. Both can increase their win without risking chips if they just fold here.

To get a better understanding of such situations, we'll take a look at the result of a potential call from your opponent. Let's assume the BB is holding pocket fives and makes the call. The value of the stacks now looks like that under the influence of the ICM (for a buy-in of $15) Hero is player 1.

If BB folds:

If BB calls and wins:

If BB calls and loses (i.e. he busts):

Now we still need to calculate the equity, villain needs to make a +$EV call.

Value of BB's stack after a fold: $479.85
Value of BB's stack after a call & win: $653.21
Value of BB's stack after a call & loss: $183.41 (prize money for place 4)

The player in the BB needs more than 63% equity, to make a +$EV call. With 55 he just has 58.52% against hero's pushing range, which is not enough.

Of course that does not mean, that you now just start pushing 100% of your hands in such situations. Your opponents calling ranges will vary depending on other factors (like your edge, blind increase, future game). The example just shows, how dramatically your pushing range could change because of the ICM influence.

But what about other push-fold situations? Is the ICM effect always as strong as in the example above? Of course not. Pushing ranges are - even if not completely independent from the ICM - relatively stable compared to calling ranges. The ranges don't change much, as long as you are not in an extreme situation like the above. That's why the lesson open pushing charts http://www.pokerstrategy.com/strategy/sng/2332/1/ uses charts to simplify the calculation of the equity.

To make that clear we look at a situation in a 9-player SNG. You are UTG and all players got around 10BB (after posting the ante). Here you find the nash ranges without ICM, based on the chip equity (every player makes +cEV decisions). The results are shown in big blinds:

Now we#ll look at the same situation with consideration of ICM. The results are shown in % of the prize pool:

You can see that there is almost no change in your pushing range, even with a pretty high risk premium. That is because your opponents need to be more cautious when calling, than you must be with your pushes. The calling ranges get tighter so you can push a bit looser. As a consequence, your ICM pushing ranges do not differ much from your chip equity pushing range. But still you need to keep your risk premium in mind.

Of course every situation is different and one small detail (like a player with a tiny stack) could change everything. That's why it is tough to give you a rule of thumb, even if the pushing ranges are in general more stable than the calling ranges, which are usually more flexible (though more dependent on the ICM).

Tell us about your experiences with such situations! How do you handle these spots?

imo it is not that sick of a spot. 180 man are top heavy there are way sicker spots with 45 man FT.

I think BB can call wider then the range you give for few reasons.
1. if you cal wider here has is great for futere spots where Hero knows that BB is not a tight caller.
2. If bb cals and wins he has a big advantage with 2 shortys who have to be tight and 1 6bb stack who really can not cal anything because of the other ones.
103s stays always push imo (especially because I think that a lot of players will go tighter then nash in SB)